From what people who experienced it told me, it's not the smell & taste loss which come from colds and similar illnesses, where your nose is runny or obstructed.
One person told me she was cleaning something with vinegar, her daughter entered the kitchen and told her "mum, this vinegar smell is horrible!" and then it dawned on her she couldn't smell anything.
No runny or stuffy nose. She was normal, except she couldn't smell anything.
At this point of the pandemic, complete loss of smell and taste of this kind almost certainly indicates covid19, outliers notwithstanding.
Trust me, I know the difference between being unable to smell/taste because your nose is blocked, and actual anosmia where you can breathe normally but the sense is just gone.
I don't know if most people experience anosmia like you describe while having a common cold or the flu, though (I think they don't). From what I've read this symptom is a pretty reliable indicator of covid19, so much so that at this time it pretty much rules out any other diagnosis and it is a strong basis for medical decision making. (Of course, there will always be outliers for any symptom. Decisions still need to be made at the population scale, though).